A comparison principle for the Lane-Emden equation and applications to geometric estimates Article Swipe
Related Concepts
Pointwise
Uniqueness
Mathematics
Maximum principle
Regular polygon
Mathematical analysis
Applied mathematics
Laplace operator
Mathematical optimization
Geometry
Optimal control
Lorenzo Brasco
,
Francesca Prinari
,
Anna Chiara Zagati
·
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2111.09603
· OA: W4226267261
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2111.09603
· OA: W4226267261
We prove a comparison principle for positive supersolutions and subsolutions to the Lane-Emden equation for the $p-$Laplacian, with subhomogeneous power in the right-hand side. The proof uses variational tools and the result applies with no regularity assumptions, both on the set and the functions. We then show that such a comparison principle can be applied to prove: uniqueness of solutions; sharp pointwise estimates for positive solutions in convex sets; localization estimates for maximum points and sharp geometric estimates for generalized principal frequencies in convex sets.
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